In a large bowl, whisk the flour, granulated sugar, baking powder, and salt until evenly combined.

In another bowl, beat the eggs lightly. Whisk in the milk, melted butter, and vanilla until smooth.

Pour the wet mixture into the dry ingredients. Stir gently with a spatula until a soft dough forms. Stop as soon as the dough comes together; do not overmix.

Lightly flour a work surface. Turn the dough out and roll it to about 1/2 inch thickness, keeping the surface and rolling pin lightly floured to prevent sticking.

Cut the dough into roughly 2 to 3 inch squares using a bench scraper or sharp knife.

Heat oil in a deep frying pan to 350°F (175°C). Use a thermometer to hold an accurate temperature.

Fry the squares in small batches for 2 to 3 minutes per side until each side is golden brown.

Transfer the beignets to a wire rack set over paper towels to drain briefly.

Dust with powdered sugar while warm and serve immediately.